Problem: Given $ m \angle BOC = 6x + 20$, $ m \angle AOB = 2x + 49$, and $ m \angle AOC = 85$, find $m\angle BOC$. $O$ $A$ $C$ $B$
Answer: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Substitute in the expressions that were given for each measure: $ {2x + 49} + {6x + 20} = {85}$ Combine like terms: $ 8x + 69 = 85$ Subtract $69$ from both sides: $ 8x = 16$ Divide both sides by $8$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 6({2}) + 20$ Simplify: $ {m\angle BOC = 12 + 20}$ So ${m\angle BOC = 32}$.